c
(c) Temperature dependence of resistivity of a conductor is given by the relation \(\rho=\) \(\rho_{0}\left[1+\alpha_{t}\left(T-T_{0}\right)\right]\)

Where \(\rho, \rho_{0}\) are resistivity at temperature \(T\) and \(T_{0}\) respectively \(\alpha_{t}\) is temperature coefficient of resistivity.

In most conductors, number density of free electrons does not change with temperature but an increase in temperature increases the amplitude of vibration of lattice ions of the metal. Therefore, the collision of free electrons with ions or atoms while drifting towards the positive end of the conductor becomes more frequent, resulting in a decrease in relaxation time. Thus resistivity of conductor increases with increase in temperature.

In semiconductor, the energy gap between the conduction band and valence band, at very low temperatures the conduction band of semiconductors are almost empty, i.e. it has no charge carriers and hence resistivity is high, but as the temperature increases more and more electrons jump to the conduction band and the resistivity decreases on account of high number of charge carriers,